I am a Platonist about properties, relations, and propositions. By this I mean that I hold that such entities actually exist, in the very same sense of the word in which tables and chairs exist, but that they, unlike the tables and chairs, do not exist in spacetime. I believe that we stand in various important relations to these "abstract" entities even though we do not share with them the advantage of not existing in spacetime. In this paper I will not say in detail why I think these entities exist. Very roughly, it is because I think they help provide the most plausible theory of various phenomena whose existence we do not question, notably the (overlapping) phenomena of belief, communication, modality1, and intentionality. My Platonism is not a matter of doctrine or dogma. If someone produces a more plausible nominalist theory of these matters, I will accept it in the same tentative spirit in which I presently accept Platonism.

I think many philosophers believe that there is a more-or-less knock-down objection to Platonism, and that their believing this has an unfortunate effect – one that sometimes hardens into dogmatism. This effect is a surprising willingness to tolerate the mysterious or obscure aspects of attempted nominalist accounts of the matters mentioned above. Instead of treating these aspects as cause for real concern and as the areas most in need of attention, such philosophers tend to pass over them in favor of grander theorizing. It is as if we already know that all that is needed is a little tidying up. Since Platonism is not regarded as a real possibility, there is an unreasonable confidence that the tidying up will be routine. Why bother with it now when there's so much more exciting stuff to think about?

The more-or-less knockdown objection to Platonism is that it cannot provide satisfactory "identity conditions" (or "identity criteria" or a "principle of individuation2") for the entities whose existence it asserts. W. V. Quine is well known for having pressed this sort of objection and his influence in the matter has been great. The goal of this paper is to argue that the demand for identity conditions is ill-conceived, not only with respect to abstract entities, but with respect to any sort of entity at all. Although various authors have noted that the notion of identity criteria is itself not very clear, the demand for criteria has been almost universally accepted, and many attempts have been made to honor the demand in various sorts of cases, notably including ships, statues3, events, and persons, as well as properties and other sorts of abstract entities.